Perturbed stochastic hereditary differential equations

• Published in: Stochastic analysis and applications Vol. 20; no. 3; pp. 567 - 589
• Main Authors: JANKOVIC, Svetlana, JOVANOVIC, Miljana
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Taylor & Francis Group 2002; Taylor & Francis
• Subjects: AMS Subject Classification: 60H10; Closeness in the (2m)th mean; Exact sciences and technology; Mathematics; Parametric perturbations; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Stochastic analysis; Stochastic differential equation; Burkholder Davis Gundy inequality; Itô equation; Differential equation; Gronwall Bellman inequality; Perturbation; Stochastic process; Parametric method; Hereditary system; Sufficient condition; Integrodifferential equation; Stochastic equation; Stochastic differential equation; Parametric perturbation

The aim of the present paper is to investigate the solution of the stochastic hereditary integrodifferential equation of Itô type with "small" perturbations which is at least a non-Markovian process, by comparing it with the solution of a simpler equation, i.e. of an unperturbed stochastic...